The creation of multipartite entangled states is a key task of quantum information processing. Among the various implementations, shortcut to adiabaticity (STA) offers a fast and robust means for generating entanglement. The traditional counterdiabatic driving, as a conventional and simple method for STA, suppresses transitions with an auxiliary Hamiltonian, but its complex interactions in many-body systems may hamper the feasibility of experimental implementation. To avoid this drawback, a flexible and efficient way was proposed theoretically by Chen et al. [Phys. Rev. A 93, 052109 (2016)] by substituting the counterdiabatic terms. Inspired by this work, we devise a practical protocol for preparing the Greenberger-Horne-Zeilinger state on the Ising spin model via STA by partial suppression of the nonadiabatic transitions, which can obviously reduce the complexity in experiments compared with the original method. We also experimentally demonstrate the viability of our scheme with a nuclear magnetic resonance quantum simulator. This work provides an alternative method to realize fast coherent quantum control for a multiqubit system in experiments.
The creation of multipartite entangled states is a key task of quantum information processing. Among the various implementations, shortcut to adiabaticity (STA) offers a fast and robust means for generating entanglement. The traditional counterdiabatic driving, as a conventional and simple method for STA, suppresses transitions with an auxiliary Hamiltonian, but its complex interactions in many-body systems may hamper the feasibility of experimental implementation. To avoid this drawback, a flexible and efficient way was proposed theoretically by Chen et al. [Phys. Rev. A 93, 052109 (2016)] by substituting the counterdiabatic terms. Inspired by this work, we devise a practical protocol for preparing the Greenberger-Horne-Zeilinger state on the Ising spin model via STA by partial suppression of the nonadiabatic transitions, which can obviously reduce the complexity in experiments compared with the original method. We also experimentally demonstrate the viability of our scheme with a nuclear magnetic resonance quantum simulator. This work provides an alternative method to realize fast coherent quantum control for a multiqubit system in experiments.
Counterdiabatic driving (CD) offers a fast and robust strategy to manipulate and prepare the quantum state in multibody systems. However, the exact CD term involving the spectral properties of the system is difficult to calculate and generally takes a complicated form for higher-dimensional complex systems. Recently, Sels and Polkovnikov [Proc. Natl. Acad. Sci. U. S. A. 114, E3909 (2017)] proposed a variational method to optimally approximate the CD term with no need for the full spectral information of the original Hamiltonian. Using a nuclear-magnetic-resonance setup, here we report an experimental demonstration of this method to construct available shortcuts to adiabaticity in a nonintegrable spin-1/2 chain via only local controls. In this process, the ground state of such a system is rapidly prepared and the final state fidelity is significantly increased compared with the traditional adiabatic method. Our experiments prove the feasibility of this variational method to design CD in practice, and thus it is a promising strategy for fast, high-fidelity quantum-state manipulation in complex and noisy quantum systems.
With the development of quantum information processing (QIP), entangled states have been used in many important fields. One of the well-known entangled states is Greenberger-Horne-Zeilinger (GHZ) state, which provides a possibility for testing quantum mechanics against local hidden theory without using Bell’s inequality. Many schemes of generating the GHZ state have been put forward in various physical systems over the past ten years. Among these physical systems, the superconducting qubits (SQs) have the potential suitability for the integrated devices in QIP and can be controlled easily through modulating electromagnetic signals and designing level configurations. On the other hand, adiabatic passage is a typical method which is used widely to generate entanglements. However, adiabatic passage needs long evolution time to satisfy the adiabatic condition. Therefore, to speed up a slow quantum adiabatic process, a new kind of technique called " shortcuts to adiabatic passage (STAP)” has attracted much attention. The Lewis-Riesenfeld invariants and transitionless quantum driving are famous methods of STAP. But they are difficult to use in the experiment. For the Lewis-Riesenfeld invariants, the driving pulses are not smoothly turned on or off and thus lead to severe impediments in experiment. For transitionless quantum driving, a direct coupling between the initial state and the target state is needed, but is too hard to obtain experimentally. In this paper, we propose a theoretical scheme for fast generating GHZ state of three superconducting qubits via superadiabatic-based shortcuts. Firstly, with the help of quantum Zeno dynamics, we obtain the effective Hamiltonian of the system, then we choose a suitable counterdiabatic Hamiltonian in the same form as the effective Hamiltonian and add it to the effective Hamiltonian in order to construct shortcuts to adiabatic passage, which can make the system evolve along one of the superadiabatic states and thus accelerate the evolution process of the system. More importantly, the superadiabatic scheme does not need an additional coupling between the initial and finial state, which ensures its high experimental feasibility. In addition, numerical simulation results show that the proposed scheme is robust against spontaneous emission, the cavity photon leakage and the dephasing of SQs.
Shortcuts to adiabaticity are well-known methods for controlling the quantum dynamics beyond the adiabatic criteria, where counterdiabatic (CD) driving provides a promising means to speed up quantum many-body systems. In this work, we show the applicability of CD driving to enhance the digitized adiabatic quantum computing paradigm in terms of fidelity and total simulation time. We study the state evolution of an Ising spin chain using the digitized version of the standard CD driving and its variants derived from the variational approach. We apply this technique in the preparation of Bell and Greenberger-Horne-Zeilinger states with high fidelity using a very shallow quantum circuit. We implement this proposal on the IBM quantum computer, proving its usefulness for the speed up of adiabatic quantum computing in noisy intermediate-scale quantum devices.
Shortcuts to adiabaticity (STA) make the fast preparation of many-body states possible, circumventing the limitations of adiabatic strategies. We propose a fast STA protocol for generating interacting states in the Tomonaga-Luttinger liquid by counterdiabatic driving, stirring the dynamics with an auxiliary control field. To this end, we exploit the equivalence between the time-dependent Tomonaga-Luttinger liquid and an ensemble of quantum oscillators with driven mass and frequency. We specify the closed-form expression of the counterdiabatic control and demonstrate its efficiency in suppressing excitations.
Using counterdiabatic (CD) driving-aiming at suppression of diabatic transition-in digitized adiabatic evolution has garnered immense interest in quantum protocols and algorithms. However, improving the approximate CD terms with a nested commutator ansatz is a challenging task. In this work, we propose a technique of finding optimal coefficients of the CD terms using a variational quantum circuit. By classical optimization routines, the parameters of this circuit are optimized to provide the coefficients corresponding to the CD terms. Then their improved performance is exemplified in Greenberger-Horne-Zeilinger state preparation on the nearest-neighbour Ising model. Finally, we also show the advantage over the usual quantum approximation optimization algorithm, in terms of fidelity with bounded time. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
Recently, the technique of counterdiabatic driving, which provides an effective strategy for accelerating adiabatic quantum evolution, has been widely applied in the preparation of many-body quantum states. In this work, we propose a theoretical scheme for the efficient preparation of Dicke states in a system of non-interacting two-level atoms. Our approach leverages the one-axis twisting (OAT) interaction to generate non-classical correlations and combines it with time-dependent external fields to achieve precise control over the dynamics of the system. By employing rapid adiabatic passage (RAP), it demonstrates how the system can be steered from an initial coherent spin state to a target Dicke state with high fidelity [S. C. Carrasco, M. H. Goerz, S. A. Malinovskaya, V. Vuletić, W. P. Schleich, and V. S. Malinovsky, Phys. Rev. Lett. \textbf{132}, 153603 (2024)]. To further optimize the preparation process, we introduce counterdiabatic driving (CD), which suppresses non-adiabatic transitions. Numerical simulations confirm that our scheme can achieve high-fidelity Dicke states for a moderate number of particles. Our results provide a scalable and experimentally feasible approach to prepare Dicke states, with potential applications in quantum metrology, quantum communication, and quantum information processing.